Parameterized complexity of the maximum independent set problem and the speed of hereditary properties

作     者：Lozin, Vadim V. 

作者机构：DIMAP Mathematics Institute University of Warwick Coventry United Kingdom 

出 版 物：《Electronic Notes in Discrete Mathematics》 (Electron. Notes Discrete Math.)

年 卷 期：2009年第34卷

页      面：127-131页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Hereditary properties Parameterized complexity Ramsey Theory 

摘      要：For a hereditary class X, the number Xn of n-vertex graphs in X (also known as the speed of X) satisfies limn → ∞ frac(log2 Xn, ((n;2))) = 1 - frac(1, k (X)) where k (X) is a natural number called the index of the class. Each class X of index k 1 can be approximated by a minimal class of the same index. In this paper, we use Ramsey theory to show that the maximum independent set problem is fixed-parameter tractable in all minimal classes of index k for all values of k. © 2009 Elsevier B.V. All rights reserved.